While I agree that having "certain" words purposely left out of everyday vocabulary, I do agree that you might be going overboard. You write that your daughter is very bright. If you explain the meaning behind these "bad words" and these words can hurt other's feelings you will tend to "head off" the situations that you want to avoid. You cannot avoid having your children overhear certain words while in the public - and believe me when I say it it inevitable that they WILL hear them in public as well.
I have always discussed anything openly with my children. At an early age, they learned that there are many words that can really hurt others feelings. Parents are "life-time" teachers for their children. As long as you teach tem as much as you can, they will be able to make informed decisions when they start making decisions on their own. IF you do not teach them the meaning behind these "bad words", they might overhear them anyway without your knowledge and use them because they did not "know" any better.
Having said that, only you and your husband should decide what and when your children should learn these "certain" words. It is up to the both of you to explain this (ever so nicely) to your Mom.
You are also correct in wanting to cherish this time as it DOES go by fast : )
A little about me:
I have 3 sons - 27 (married with a very sucessful career), 19 (never been in trouble and just getting out on his own), 11 (very bright, straight-A student looking forward to becoming a Paleontologist since he was 3). My husband and I are very fortunate for having 3 wonderful sons!